1) To divide 4 2/3 by 2/9, first convert the mixed number to an improper fraction:
4 2/3 = (4*3 + 2)/3 = 14/3

Now, divide 14/3 by 2/9:
(14/3) ÷ (2/9)
= (14/3) * (9/2)
= 126/6
= 21

Therefore, 4 2/3 ÷ 2/9 = 21.

2) To divide 6 1/4 by 5/8, first convert the mixed number to an improper fraction:
6 1/4 = (6*4 + 1)/4 = 25/4

Now, divide 25/4 by 5/8:
(25/4) ÷ (5/8)
= (25/4) * (8/5)
= 200/20
= 10

Therefore, 6 1/4 ÷ 5/8 = 10.